In a small bowl, whisk together mayonnaise, tarragon and lemon juice until combined.

On each flatbread, spread about 2 tablespoons of the mayonnaise mixture on top. Scatter each flatbread with an even amount of the lettuce and tomatoes. Crumble 2 bacon slices, per serving, over the lettuce and tomatoes. Sprinkle an even amount of chicken on top of the bacon. Carefully roll each flatbread up and cut in half to serve.